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 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,