Internal problem ID [10932]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 20(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 100
dsolve((2*sin(x)-cos(x))*diff(y(x),x$2)+(7*sin(x)+4*cos(x))*diff(y(x),x)+10*y(x)*cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\left (\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{-2 \sin \left (x \right )+\cos \left (x \right )}d x \right )}+c_{2} {\mathrm e}^{-\left (\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{-2 \sin \left (x \right )+\cos \left (x \right )}d x \right )} \left (\int -\frac {\csc \left (x \right ) {\mathrm e}^{\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{-2 \sin \left (x \right )+\cos \left (x \right )}d x}}{-2 \sin \left (x \right )+\cos \left (x \right )}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.997 (sec). Leaf size: 95
DSolve[(2*Sin[x]-Cos[x])*y''[x]+(7*Sin[x]+4*Cos[x])*y'[x]+10*y[x]*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \int _1^{e^{i x}}\frac {e^{-3 i \arctan \left (2-\frac {4}{K[1]^2+1}\right )} K[1]^{-2+2 i} \left ((1+2 i) K[1]^2+(1-2 i)\right )^4}{\left (5 K[1]^4-6 K[1]^2+5\right )^{3/2}}dK[1]+c_1}{4 (\cos (x)-2 \sin (x))^2} \\ \end{align*}