Internal problem ID [6019]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 6.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(y(x),x)^2-(x^2*y(x)+3)*diff(y(x),x)+3*x^2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \\ y \relax (x ) = 3 x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 27
DSolve[(y'[x])^2-(x^2*y[x]+3)*y'[x]+3*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {x^3}{3}} \\ y(x)\to 3 x+c_1 \\ \end{align*}