Correct option :(B) According to ques, \[y~=\text{ }A\text{ }cos\text{ }ax~+\text{ }B\text{ }sin\text{ }ax\] Differentiating with respect to x,
If y = e–x (A cos x + B sin x), then y is a solution of: (A) d^2y/dx^2+2dy/dx=0 (B)d^2y/dx^2-2dy/dx+2y=0 (C)d^2y/dx^2+2dy/dx=2y=0 (D)d^y/dx^2+2y=0
Correct option :(C). According to ques, \[y~=~{{e}^{x}}~\left( A\text{ }cos~x~+\text{ }B\text{ }sin~x \right)\] Differentiating both sides with respect to x,
The order and degree of the differential equation d^2y/dx^2=(dy/dx)^1/4+x^1/5=0 respectively, are (A) 2 and not defined (B) 2 and 2 (C) 2 and 3 (D) 3 and 3
Correct option : (A) 2 and not defined According to ques, Since the degree of dy/dx is in fraction its undefined and the degree is \[2.\]
Choose the correct answer from the given four options: The degree of the differential equation [1+(dy/dx)^2]^3/2=d^2y/dx^2 is (A) 4 (B) 3/2 (C) not defined (D) 2
Correct option: D (2) According to ques, hence the answer is 2.
Choose the correct answer from the given four options. The degree of the differential equation (d^2y/dx^2)^2+(dy/dx)^2=xsin(dy/dx)is: (A) 1 (B) 2 (C) 3 (D) not defined
Correct option: (D) not defined. As the value of sin (dy/dx) on expansion will be in increasing power of dy/dx,
Solve : x dy/dx (log y-logx+1)
According to ques,
Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P (x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.
Let \[P\left( x\text{ },\text{ }y \right)\] be any point on the curve, AB be the tangent to the given curve at P. A/Q, P is the mid-point of AB HENCE, the coordinates of \[A\text{ }is\text{ }\left(...
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abscissa and ordinate of the point.
According to the ques, The slope of the tangent of the curve \[=\text{ }dy/dx\] Now, the difference between the abscissa and ordinate \[=\text{ }x\text{ }\text{ }y\] Hence A/Q, \[dy/dx\text{...
Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is (y – 1)/ (x2 + x)
According to ques, Since, the line is passing through the point (1, 0), then \[\left( 0\text{ }\text{ }1 \right)\text{ }\left( 1\text{ }+\text{ }1 \right)\text{ }=\text{ }c\left( 1...
Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is (y – 1)/ (x2 + x)
ACCORDING TO QUES, Line is passing through the point \[\left( 1,\text{ }0 \right),SO,\] \[\left( 0\text{ }\text{ }1 \right)\text{ }\left( 1\text{ }+\text{ }1 \right)\text{ }=\text{ }c\left( 1...
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is (x2 + y2)/ 2xy.
ACCORDING TO QUES, It’s a homogeneous differential function,
Find the general solution of dy/dx – 3y = sin 2x.
According to ques, \[~P\text{ }=\text{ }-3\text{ }and\text{ }Q\text{ }=\text{ }sin\text{ }2x\]
Solve: dy/dx = cos(x + y) + sin (x + y). [Hint: Substitute x + y = z]
According to ques,
Find the general solution of (1 + tan y) (dx – dy) + 2xdy = 0.
according to ques,
Solve :
according to the ques,
Find the differential equation of system of concentric circles with centre (1, 2).
according to ques, concentric circles with centre \[\left( 1,\text{ }2 \right)\] and with radius ‘r’ can be written as, \[{{\left( x\text{ }\text{ }1 \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{...
Solve the differential equation (1 + y2) tan–1x dx + 2y (1 + x2) dy = 0.
ACCORDING TO QUES, \[~\left( 1\text{ }+~{{y}^{2}} \right)\text{ }ta{{n}^{1}}x\text{ }dx~+\text{ }2y~\left( 1\text{ }+~{{x}^{2}} \right)~dy~=\text{ }0\] \[2y\text{ }\left( 1\text{ }+\text{ }{{x}^{2}}...
Form the differential equation by eliminating A and B in Ax2 + By2 = 1.
ACCORDING TO QUES, DIFFERENTIATING WITH RESPECT TO x ,
Solve the differential equation dy = cos x (2 – y cosec x) dx given that y = 2 when x = π/2.
according to ques,
Solve : 2 (y + 3) – xy dy/dx = 0, given that y(1) = -2.
according to ques,
Solve : (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy]
According to ques, or, \[\left( x~+~y \right)\text{ }\left( dx~~dy \right)\text{ }=~dx~+~dy\] \[\left( x\text{ }+\text{ }y \right)\text{ }dx\text{ }\text{ }\left( x\text{ }\text{ }y \right)\text{...
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
according to ques,
Find the general solution of the differential equation:(1+y^2)+(x-e^tan-1y)dy/dx=0.
according to ques,
Solve: x^2dy/dx=x^2+xy+y^2
according to ques,
Find the equation of a curve passing through origin and satisfying the differential equation: (1+x^2)dy/dx+2xy=4x^2
according to ques,
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
According to ques, Equation will be, \[{{\left( x\text{ }\text{ }0 \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{ }a \right)}^{2}}~=\text{ }{{a}^{2}},\] where (0, a) is the centre...
Form the differential equation having y = (sin–1x)2 + A cos–1x + B, where A and B are arbitrary constants, as its general solution.
according to ques,
If y(t) is a solution of and y (0) = – 1, then show that y (1) = -1/2.
according to ques,
If y(x) is a solution of and y (0) = 1, then find the value of y(π/2).
according to ques,
Find the general solution of (x + 2y3) dy/dx = y.
according to ques,
Solve the differential equation dy/dx = 1 + x + y2 + xy2, when y = 0, x = 0.
according to ques, we can write,
Solve: ydx – xdy = x2ydx.
According to ques we have, \[~ydx\text{ }\text{ }xdy\text{ }=\text{ }{{x}^{2}}ydx\] or, \[y\text{ }dx\text{ }\text{ }{{x}^{2}}y\text{ }dx\text{ }=\text{ }xdy\] \[y\text{ }\left( 1\text{ }\text{...
Solve the differential equation: dy/dx+1=e^x+y
ACCORDING TO QUES, \[dy/dx\text{ }+\text{ }1\text{ }=\text{ }{{e}^{x+y}}\] NOW PUTTING, \[x\text{ }+\text{ }y\text{ }=\text{ }t\] and differentiating w.r.t. x,
Find the general solution of: dy/dx+ay=e^mx
ACCORDING TO QUES, \[dy/dx\text{ }+\text{ }ay\text{ }=\text{ }{{e}^{mx}}\] for linear differential equation of first order, \[P\text{ }=\text{ }a\text{ }and\text{ }Q\text{ }=\text{...
Solve the differential equation: dy/dx+2xy=y
according to ques, \[dy/dx\text{ }+\text{ }2xy\text{ }=\text{ }y\]
Solve the differential equation: (x^2-1)dy/dx+2xy=1/x^2-1
according to ques,
Given that dy/dx=e^-2y and y = 0 when x = 5. Find the value of x when y = 3.
according to ques,
Find the differential equation of all non-vertical lines in a plane.
SINCE ,equation of all non-vertical lines is $$ \[~y\text{ }=\text{ }mx\text{ }+\text{ }c\] On differentiating w.r.t. x, \[dy/dx\text{ }=\text{ }m\] and, on differentiating w.r.t. x,...
Find the solution of : dy/dx = 2^y-x
ACCORDING TO QUES,