Solve the following differential equations: y y= ( y^2-x ) d y d … - Vidyadip

Question

Solve the following differential equations:

$y \log y=\left(\log y^2-x\right) \frac{d y}{d x}$

✓

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.(5 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

Find the mean, variance and standard deviation of the number of tails in three tosses of a coin.

Find the inverse of the following matrices:$\begin{bmatrix}1 & 2 & 3 \\ 2 & 3 & 1\\ 3 & 1 & 2 \end{bmatrix}$

If $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right],$ find $A ^{-1}$ by the adjoint method.

Evaluate the following integrals:$\int^\limits1_0\sqrt{\frac{1-\text{x}}{1+\text{x}}}\text{ dx}$

Solve the following system of equations by matrix method:
$5x + 7y + 2 = 0$

$4x + 6y + 3 = 0$

If $x ^2+6 xy + y ^2=10$, show that $\frac{d^2 y}{d x^2}=\frac{80}{(3 x+y)^3}$

Evaluate the following integrals:$\int^\limits{(\pi)^\frac{2}{3}}_{0}\sqrt{\text{x}}\cos^2\text{x}^{\frac{3}{2}}\text{ dx}$

If $\text{x}=10(\text{t}-\sin\text{t}),\text{y}=12(1-\cos\text{t}),$ find $\frac{\text{dy}}{\text{dx}}.$

Prove that:
$\begin{vmatrix}\text{z}&\text{x}&\text{y}\\\text{z}^2&\text{x}^2&\text{y}^2\\\text{z}^4&\text{x}^4&\text{y}^4 \end{vmatrix}=\begin{vmatrix}\text{x}&\text{y}&\text{z}\\\text{x}^2&\text{y}^2&\text{z}^2\\\text{x}^4&\text{y}^4&\text{z}^4 \end{vmatrix}=\begin{vmatrix}\text{x}^2&\text{y}^2&\text{z}^2\\\text{x}^4&\text{y}^4&\text{z}^2\\\text{x}&\text{y}&\text{z}\end{vmatrix}$
$=\text{xyz}(\text{x}-\text{y})(\text{y}-\text{z})(\text{z}-\text{x})(\text{x}+\text{y}+\text{z}).$

Show that the family of curves for which $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^2+\text{y}^2}{2\text{xy}},$ is given by $\text{x}^2-\text{y}^2=\text{Cx}$