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.

$y=3 \cos (\log x)+4 \sin (\log x) ; x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}+y=0$

✓

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.(4 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

A box with a square base is to have an open top. The surface area of the box is $192$ sq cm. What should be its dimensions in order that the volume is largest?

$a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13} = |A|$

Find the inverse of the matrix,
$A=\left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right]$ using elementary row transformations.

Find the area of sector of circle bounded by $x^2+y^2=16$ and the line $y=x$. in the first quadrant.

Find the nth derivative of the following:
cos x

Find the points on the curve $y=x^3-2 x^2-x$ where the tangents are parallel to $3 x-y+1=$

0.

$\int x^3 \tan ^{-1} x d x$

Find the vector and Cartesian equations of the plane passing through the points $A (1,1,-2), B (1,2,1)$ and $C (2,-1,1)$

Express $-\hat{ i }-3 \hat{ j }+4 \widehat{ k }$ as the linear combination of the vectors $2 \hat{ i }+\hat{ j }-4 \widehat{ k }, 2 \hat{ i }-\hat{ j }+3 \widehat{ k }$ and $3 \hat{ i }+\hat{ j }-2 \widehat{ k }$

Show that the equation $x^2-6 x y+5 y^2+10 x-14 y+9=0$ represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines.