28.1.136 problem 159

Internal problem ID [4442]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 159
Date solved : Monday, January 27, 2025 at 09:17:39 AM
CAS classification : [`x=_G(y,y')`]

\begin{align*} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-x^{2} y^{2}-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

dsolve((2*x*y(x)^4*exp(y(x))+2*x*y(x)^3+y(x))+(x^2*y(x)^4*exp(y(x))-x^2*y(x)^2-3*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {x^{2} {\mathrm e}^{y \left (x \right )} y \left (x \right )^{3}+y \left (x \right )^{3} c_{1} +x^{2} y \left (x \right )^{2}+x}{y \left (x \right )^{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.308 (sec). Leaf size: 29

DSolve[(2*x*y[x]^4*Exp[y[x]]+2*x*y[x]^3+y[x])+(x^2*y[x]^4*Exp[y[x]]-x^2*y[x]^2-3*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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