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]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x)=exp(x)*sin(x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}+\frac {\left (-\cos \relax (x )+\sin \relax (x )\right ) {\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.021 (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*}