Internal problem ID [11663]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y^{\prime } x +y-\left (y x \right )^{\frac {3}{2}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 9
dsolve([x*diff(y(x),x)+y(x)=(x*y(x))^(3/2),y(1) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {4}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 24
DSolve[{x*y'[x]+y[x]==(x*y[x])^(3/2),{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{x^3} \\ y(x)\to \frac {4}{(x-2)^2 x} \\ \end{align*}