27.24 problem 790

Internal problem ID [4030]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 27
Problem number: 790.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

\[ \boxed {{y^{\prime }}^{2}+2 x y^{\prime }=3 x^{2}} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 21

dsolve(diff(y(x),x)^2+2*x*diff(y(x),x)-3*x^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) = \frac {x^{2}}{2}+c_{1} y \left (x \right ) = -\frac {3 x^{2}}{2}+c_{1} \end{align*}

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[(y'[x])^2+2 x y'[x]-3 x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 x^2}{2}+c_1 y(x)\to \frac {x^2}{2}+c_1 \end{align*}