Solve the differential equation : y-x d y d x =0 - Vidyadip

Question

Solve the differential equation : $y-x \frac{d y}{d x}=0$

✓

Answer

$\begin{aligned} & y-x \frac{d y}{d x}=0 \\ & \therefore y=x \frac{d y}{d x} \\ & \therefore \frac{d x}{x}=\frac{d y}{y}\end{aligned}$
Integrating on both sides, we get
$\int \frac{d x}{x}=\int \frac{d y}{y}$
∴ log |x| = log |y| + log |c|
∴ log |x| = log |cy|
∴ x = cy

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.(2 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

Which of the following represents direction cosines of a lines

Write the orincipal value of $\cos^{-1}(\cos680^\circ)$

If $\vec{\text{r}}=\text{x}\hat{\text{i}}+\text{y}\hat{\text{j}}+\text{z}\hat{\text{k}},$ then write the value of $\big|\vec{\text{r}}\times\hat{\text{i}}\big|^2.$

If A is a square matrix of order $3$ such that $|A| = 2$, then write the value of adj (adj A).

Find x, y satisfying the matrix equation.
$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$

Construct the truth table for each of the following : ~(~p ∧ ~q) ∨ q

If $\text{A}=\begin{bmatrix}0&\text{i}\\\text{i}&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}0&1\\1&0\end{bmatrix},$ find the value of $|\text{A}|+|\text{B}|.$

Evaluate the following:

$\int \cos (\sqrt[3]{x}) d x$

If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=144$ and $|\vec{\text{a}}|=4,$ find $\big|\vec{\text{b}}\big|.$

Find the components along the coordinate axis of the position vector of the following point:S(4,-3)