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verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[~\mathbf{y}\text{ }=\text{ }{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{C}\text{ }:\text{ }\mathbf{y}\prime \text{ }\text{ }-\mathbf{2x}\text{ }\text{ }-\mathbf{2}\text{ }=\text{ }\mathbf{0}\]
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[~\mathbf{y}\text{ }=\text{ }{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{C}\text{ }:\text{ }\mathbf{y}\prime \text{ }\text{ }-\mathbf{2x}\text{ }\text{ }-\mathbf{2}\text{ }=\text{ }\mathbf{0}\]
CBSE | Class 12 | Differential Equations | Exercise 9.2 | NCERT
verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \[~\mathbf{y}\text{ }=\text{ }{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }+\text{ }\mathbf{C}\text{ }:\text{ }\mathbf{y}\prime \text{ }\text{ }-\mathbf{2x}\text{ }\text{ }-\mathbf{2}\text{ }=\text{ }\mathbf{0}\]

Differentiating both sides with respect to x, we get,

NCERT Solutions for Class 12 Maths Chapter 9 - Image 13

y’ = 2x + 2

Substituting the values of y’ in the given differential equations, we get,

\[\begin{array}{*{35}{l}}

=\text{ }y\text{ }-\text{ }2x\text{ }-2  \\

=\text{ }2x\text{ }+\text{ }2-\text{ }\text{ }2x\text{ }-\text{ }2  \\

=\text{ }0  \\

\end{array}\]

 

= RHS

Therefore, the given function is a solution of the given differential equation.

i

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