Solve differential equationy'+y/x= 3y^(-2) x>0

Solve differential equationy'+y/x= 3y^(-2) x>0


Solve differential equation \(y'+y/x= 3y^{-2}\) \(x>0\)

Answers (1)


Dividing both sidesby \(y^{-2}\)
\(y^2y'+ y^3/x=3\)
Differentiating both sides with respect to x
\(du/dx= 3y^2 dy/dx\)
\(1/3 (du)/dx= y^2 dy/dx\)
Substituting this in the equation \(y^2y'+ y^3/x=3\)
Substituting \(1/3 (du)/dx= y^2 dy/dx\) and \(u=y^3\) in the equation \(y^2y'+ y^3/x=3\)
\(1/3 (du)/dx+ u/x=3\)
\(1/9 (du)/dx+u/(3x)=1\)


Relevant Questions

asked 2021-03-07

Solve differential equation \(\frac{\cos^2y}{4x+2}dy= \frac{(\cos y+\sin y)^2}{\sqrt{x^2+x+3}}dx\)

asked 2020-10-23

Write the first order differential equation for \(y=2-\int_0^x(1+y(t))\sin tdt\)

asked 2020-11-23

Write an equivalent first-order differential equationand initial condition for y \(y= 1+\int_0^x y(t) dt\)

asked 2021-01-13

Solve differential equation \(dy+5ydx=e^{-5x}dx\)

asked 2021-02-21

The coefficient matrix for a system of linear differential equations of the form \(\displaystyle{y}^{{{1}}}={A}_{{{y}}}\) has the given eigenvalues and eigenspace bases. Find the general solution for the system.
\(\left[\lambda_{1}=-1\Rightarrow\left\{\begin{bmatrix}1 0 3 \end{bmatrix}\right\},\lambda_{2}=3i\Rightarrow\left\{\begin{bmatrix}2-i 1+i 7i \end{bmatrix}\right\},\lambda_3=-3i\Rightarrow\left\{\begin{bmatrix}2+i 1-i -7i \end{bmatrix}\right\}\right]\)

asked 2020-10-23

Determine whether the ordered pair is a solution to the given system of linear equations.
\(\left\{\begin{matrix} 3x−y=1 \\ 2x+3y=8 \end{matrix}\right\}\)

asked 2021-02-09

What is the process to solve these:
Vertex, \(y-\int\)., \(x-\int\), graph \(= -(x+1)^2+1\)

asked 2021-02-14

Find the solution (x,y)to the system of equations.
\(\begin{cases}3x + y = 28\\-x+3y=4\end{cases}\)
Multiply the coordinates \(x \cdot y\)

asked 2021-02-02

Let \(\displaystyle{f{{\left({x},{y}\right)}}}=-\frac{{{x}{y}}}{{{x}^{{2}}+{y}^{{2}}}}\).
Find limit of \(f(x,y)\ \text{as}\ (x,y)\ \rightarrow (0,0)\ \text{i)Along y axis and ii)along the line}\ y=x.\ \text{Evaluate Limes}\ \lim_{x,y\rightarrow(0,0)}y\log(x^{2}+y^{2})\),by converting to polar coordinates.

asked 2021-03-10

Solve the system of equations: