Internal problem ID [10279]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\sin \relax (x ) y^{\prime \prime }+2 y^{\prime } \cos \relax (x )+3 \sin \relax (x ) y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(sin(x)*diff(y(x),x$2)+2*cos(x)*diff(y(x),x)+3*sin(x)*y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (2 x \right ) c_{2}}{\sin \relax (x )}+\frac {\cos \left (2 x \right ) c_{1}}{\sin \relax (x )}+\frac {{\mathrm e}^{x}}{5 \sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 56
DSolve[Sin[x]*y''[x]+2*Cos[x]*y'[x]+3*Sin[x]*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-i x} \left (4 i e^{(1+2 i) x}+5 c_2 e^{4 i x}+20 i c_1\right )}{10 \left (-1+e^{2 i x}\right )} \\ \end{align*}