7.7.4 problem 4

Internal problem ID [182]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 4
Date solved : Friday, February 07, 2025 at 08:01:39 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 20

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

\[ x^{2} y^{3}+{\mathrm e}^{x}-\cos \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 23

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

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