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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 14 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 14 Maths Textbook Solution.

Answers (1)

Answer: Thus  : y=A\cos x+\sin x   is the solution of the given differential equation

Hint: Solve first order derivative and put values in differential equation to be verified.

Given:y=A\cos x+\sin x,\cos x\frac{dy}{dx}+\left ( sinx \right )y=1

Solution:

\frac{dy}{dx}=A\sin x+\cos x …Differentiating w.r.t to x,

Now, differential eq.

\begin{aligned} &\text { L. } H . S=\operatorname{cos} x\left(\frac{d y}{d x}\right)+(\operatorname{sin} x) y \\ &\operatorname{cos} x(-A \operatorname{sin} x+\operatorname{cos} x)+\operatorname{sin} x(A \operatorname{cos} x+\operatorname{sin} x) \\ &-A \operatorname{sin} x \operatorname{cos} x+\operatorname{cos}^{2} x+A \operatorname{sin} x \operatorname{cos} x+\operatorname{sin}^{2} x \\ &\operatorname{cos}^{2} x+\operatorname{sin}^{2} x=1=R . H . S \ldots\left\{\operatorname{cos}^{2} x+\operatorname{sin}^{2} x=1\right\} \end{aligned}

Hence, Proved.

 

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