Internal problem ID [13452]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.15 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(x^2*diff(y(x),x$2)-2*y(x)=15*cos(3*ln(x))-10*sin(3*ln(x)),y(x), singsol=all)
\[ y = \sin \left (\frac {3 \ln \left (x \right )}{2}\right ) \cos \left (\frac {3 \ln \left (x \right )}{2}\right )-3 \cos \left (\frac {3 \ln \left (x \right )}{2}\right )^{2}+\frac {3}{2}+\frac {c_{1}}{x}+c_{2} x^{2} \]
✓ Solution by Mathematica
Time used: 0.154 (sec). Leaf size: 35
DSolve[x^2*y''[x]-2*y[x]==15*Cos[3*Log[x]]-10*Sin[3*Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^2+\frac {c_1}{x}+\frac {1}{2} (\sin (3 \log (x))-3 \cos (3 \log (x))) \]