Internal problem ID [1932]
Book: Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section: Exercis 2, page 5
Problem number: 3(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } \sin \left (y\right )-x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)*sin(y(x))=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \pi -\arccos \left (\frac {x^{3}}{3}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.448 (sec). Leaf size: 37
DSolve[y'[x]*Sin[y[x]]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {x^3}{3}-c_1\right ) \\ y(x)\to \arccos \left (-\frac {x^3}{3}-c_1\right ) \\ \end{align*}