15.16.10 problem 10

Internal problem ID [3230]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:26:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=4*x+sin(ln(x)),y(x), singsol=all)
 

\[ y = \frac {3 \cos \left (\ln \left (x \right )\right )}{10}+\frac {\sin \left (\ln \left (x \right )\right )}{10}-4 x \ln \left (x \right )+c_2 \,x^{2}+\left (c_{1} -4\right ) x \]

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 33

DSolve[x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==4*x+Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} (\sin (\log (x))+3 \cos (\log (x))+10 x (-4 \log (x)+c_2 x-4+c_1)) \]