Internal problem ID [13451]
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 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=85 \cos \left (2 \ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=85*cos(2*ln(x)),y(x), singsol=all)
\[ y = \frac {c_{2} +\int \frac {c_{1} +17 \cos \left (2 \ln \left (x \right )\right ) x +34 x \sin \left (2 \ln \left (x \right )\right )}{2 x^{\frac {3}{2}}}d x}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 34
DSolve[2*x^2*y''[x]+5*x*y'[x]+y[x]==85*Cos[2*Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x}+\frac {c_2}{\sqrt {x}}+6 \sin (2 \log (x))-7 \cos (2 \log (x)) \]