73.15.77 problem 22.15 (d)

Internal problem ID [15508]
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)
Date solved : Tuesday, January 28, 2025 at 08:00:28 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 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 ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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)
 

\[ y = \frac {c_{1}}{x}+c_{2} x^{2}-\frac {3 \cos \left (3 \ln \left (x \right )\right )}{2}+\frac {\sin \left (3 \ln \left (x \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 80

DSolve[x^2*D[y[x],{x,2}]-2*y[x]==15*Cos[3*Log[x]]-10*Sin[3*Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3 \int _1^x\frac {5 (3 \cos (3 \log (K[2]))-2 \sin (3 \log (K[2])))}{3 K[2]^3}dK[2]+\int _1^x\left (\frac {10}{3} \sin (3 \log (K[1]))-5 \cos (3 \log (K[1]))\right )dK[1]+c_2 x^3+c_1}{x} \]