Internal problem ID [6772]
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]
\[ \boxed {{y^{\prime }}^{2}-\left (y x^{2}+3\right ) y^{\prime }+3 y x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) &= c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \\ y \left (x \right ) &= 3 x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (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*}