Internal problem ID [2508]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-{\mathrm e}^{x} \sin \left (x \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(x),x)=exp(x)*sin(x),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{2}+\frac {{\mathrm e}^{x} \left (-\cos \left (x \right )+\sin \left (x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[{y'[x]==Exp[x]*Sin[x],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^x (\sin (x)-\cos (x))+1\right ) \\ \end{align*}