Internal problem ID [5492]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 2(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }-y^{2} y^{\prime }-\left (y^{\prime }\right )^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = -{\frac {1}{2}}, y^{\prime }\relax (0) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.343 (sec). Leaf size: 16
dsolve([y(x)*diff(y(x),x$2)=y(x)^2*diff(y(x),x)+(diff(y(x),x))^2,y(0) = -1/2, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3}{8 \,{\mathrm e}^{\frac {3 x}{2}}-2} \]
✓ Solution by Mathematica
Time used: 0.913 (sec). Leaf size: 20
DSolve[{y[x]*y''[x]==y[x]^2*y'[x]+(y'[x])^2,{y[0]==-1/2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{2-8 e^{3 x/2}} \\ \end{align*}