62.30.5 problem Ex 5

Internal problem ID [12969]
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
Date solved : Tuesday, January 28, 2025 at 04:45:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 28

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)
 

\[ y = \frac {\csc \left (x \right ) \left (10 c_{1} \cos \left (x \right )^{2}+10 \sin \left (x \right ) \cos \left (x \right ) c_{2} +{\mathrm e}^{x}-5 c_{1} \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 56

DSolve[Sin[x]*D[y[x],{x,2}]+2*Cos[x]*D[y[x],x]+3*Sin[x]*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-i x} \left (4 i e^{(1+2 i) x}+5 c_2 e^{4 i x}+20 i c_1\right )}{10 \left (-1+e^{2 i x}\right )} \]