60.3.182 problem 1186

Internal problem ID [11192]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1186
Date solved : Monday, January 27, 2025 at 10:48:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

dsolve(x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x)-sin(x)*x^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 51

DSolve[-(x^3*Sin[x]) + 8*y[x] - 5*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 \left (2 \int _1^x-\frac {1}{2} \sin (K[1])dK[1]+x^2 \operatorname {CosIntegral}(x)+2 c_2 x^2-x \sin (x)+2 c_1\right ) \]