35.4.4 problem 4

Internal problem ID [6122]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 4
Date solved : Monday, January 27, 2025 at 01:36:42 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 22

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

\[ x^{2} {\mathrm e}^{3 y}+{\mathrm e}^{x}-\frac {y^{3}}{3}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.269 (sec). Leaf size: 28

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

\[ \text {Solve}\left [x^2 e^{3 y(x)}-\frac {1}{3} y(x)^3+e^x=c_1,y(x)\right ] \]