CBSE Class 12 Mathematics sample paper 2023-24: question 29(b)

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Divide by ${\cos }^{2}x$: $\frac{dy}{dx}+y{\sec }^{2}x=\tan x{\sec }^{2}x$. This is linear, with $P={\sec }^{2}x$ and $Q=\tan x{\sec }^{2}x$.

   ½ mark

2. I.F. $=e^{\int {\sec }^{2}xdx}=e^{\tan x}$.

   ½ mark

3. Solution: $y{e}^{\tan x}=\int e^{\tan x}\tan x{\sec }^{2}xdx$. Put $t=\tan x$, $dt={\sec }^{2}xdx$: $\int t{e}^{t}dt=t{e}^t-e^t+C$.

   1 mark

4. So $y{e}^{\tan x}=(\tan x-1)e^{\tan x}+C$, i.e. $y=\tan x-1+C{e}^{-\tan x}$.

   1 mark

Answer: $y=\tan x-1+C{e}^{-\tan x}$

Revise the chapter

• Chapter: Differential Equations (notes, formulas, where marks are lost and every past question)
• Topic: Linear Differential Equations