Internal problem ID [4182]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 948.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 91
dsolve(y(x)*diff(y(x),x)^2+x^3*diff(y(x),x)-x^2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {i x^{2}}{2} y \left (x \right ) = \frac {i x^{2}}{2} y \left (x \right ) = 0 y \left (x \right ) = -\frac {\sqrt {-4 c_{1} x^{2}+c_{1}^{2}}}{4} y \left (x \right ) = \frac {\sqrt {-4 c_{1} x^{2}+c_{1}^{2}}}{4} y \left (x \right ) = -\frac {2 \sqrt {c_{1} x^{2}+4}}{c_{1}} y \left (x \right ) = \frac {2 \sqrt {c_{1} x^{2}+4}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 1.28 (sec). Leaf size: 244
DSolve[y[x] (y'[x])^2+x^3 y'[x]-x^2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {\sqrt {x^6+4 x^2 y(x)^2} \log \left (\sqrt {x^4+4 y(x)^2}+x^2\right )}{2 x \sqrt {x^4+4 y(x)^2}}+\frac {1}{2} \left (1-\frac {\sqrt {x^6+4 x^2 y(x)^2}}{x \sqrt {x^4+4 y(x)^2}}\right ) \log (y(x))=c_1,y(x)\right ] \text {Solve}\left [\frac {1}{2} \left (\frac {\sqrt {x^6+4 x^2 y(x)^2}}{x \sqrt {x^4+4 y(x)^2}}+1\right ) \log (y(x))-\frac {\sqrt {x^6+4 x^2 y(x)^2} \log \left (\sqrt {x^4+4 y(x)^2}+x^2\right )}{2 x \sqrt {x^4+4 y(x)^2}}=c_1,y(x)\right ] y(x)\to -\frac {i x^2}{2} y(x)\to \frac {i x^2}{2} \end{align*}