53.1.6 problem 6

Internal problem ID [8440]
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
Date solved : Monday, January 27, 2025 at 04:00:49 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \\ y &= 3 x +c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 27

DSolve[(D[y[x],x])^2-(x^2*y[x]+3)*D[y[x],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*}