In each of the following examples verify that the given function … - Vidyadip

Question

In each of the following examples verify that the given function is a solution of the differential equation.

$xy = ae ^{ x }+ be ^{- x }+ x ^2 ; x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}+x^2=x y+2$

✓

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate: $\int_{-1}^1|5 x-3| d x$

Prove that the given vectors are coplanar:
$2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},\ \hat{\text{i}}-3\hat{\text{j}}-5\hat{\text{k}}$ and $3\hat{\text{i}}-4\hat{\text{j}}-4\hat{\text{k}}$

Find the inverse of each of the following matrices $($if they exist$) : \left[\begin{array}{ll}2 & 1 \\ 1 & -1\end{array}\right]$

Show that $\text{f}(\text{x})=\cos^2\text{x}$ is a decreasing function on $\Big(0,\frac{\pi}{2}\Big).$

If A and B are events such that P(A) = 0.6, P(B) = 0.3 and $\text{P}(\text{A}\cap\text{B})=0.2$ find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ and $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big).$

Evaluate the following integrals:
$\int\text{e}^{\text{x}}\Big(\frac{1}{\text{x}^2}-\frac{2}{\text{x}^3}\Big)\text{dx}$

Find the vector equation of the plane with intercepts 3, -4 and 2 on x, y and z-axis respectively.

For the principal values, evaluate the following:
$\sin^{-1}\Big(-\frac{1}{2}\Big)+2\cos^{-1}\Big(-\frac{\sqrt3}{2}\Big)$

Find the length of the perpendicular drow from the point (5, 4, -1) to the line $\vec{\text{r}}=\hat{\text{i}}+\lambda\big(2\hat{\text{i}}+9\hat{\text{j}}+5\hat{\text{k}}\big).$

Evaluate the following definite integrals:$\int_{1}^\limits{2}\text{e}^{2\text{x}}\Big(\frac{1}{\text{x}}-\frac{1}{2\text{x}^2}\big)\text{dx}$