Differential Equations
Linear ODE — First Order
nta_pyq_2024_apr
Grade 12
Question:
Let the solution $y=y(x)$ of the differential equation $\dfrac{dy}{dx}-y=1+4\sin x$ satisfy $y(\pi)=1$. Then $y\left(\dfrac{\pi}{2}\right)+10$ is equal to ________.
Step-by-Step Solution
Key Concept: Linear ODE, IF $=e^{-x}$. Solution: $ye^{-x}=\int(1+4\sin x)e^{-x}dx$. Integrate by parts.
$y=-1-2(\sin x+\cos x)$. $y(\pi/2)=-3$. $y(\pi/2)+10=7$.
Correct Answer: 7