Internal problem ID [4479]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page
64
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {{\mathrm e}^{x} \sin \left (y\right )-3 x^{2}+\left ({\mathrm e}^{x} \cos \left (y\right )+\frac {1}{3 y^{\frac {2}{3}}}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((exp(x)*sin(y(x))-3*x^2)+(exp(x)*cos(y(x))+y(x)^(-2/3)/3)*diff(y(x),x)=0,y(x), singsol=all)
\[ {\mathrm e}^{x} \sin \left (y \left (x \right )\right )-x^{3}+y \left (x \right )^{\frac {1}{3}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.421 (sec). Leaf size: 28
DSolve[(Exp[x]*Sin[y[x]]-3*x^2)+(Exp[x]*Cos[y[x]]+y[x]^(-2/3)/3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-3 x^3+3 \sqrt [3]{y(x)}+3 e^x \sin (y(x))=c_1,y(x)\right ] \]