15.4.5 problem 5

Internal problem ID [2918]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:55:45 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 32

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

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