40.12.3 problem 8

Internal problem ID [6751]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre). Supplemetary problems. Page 110
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:27:30 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)=x+sin(ln(x)),y(x), singsol=all)
 

\[ y = -c_1 \ln \left (x \right )+\ln \left (x \right ) x +c_2 x +c_3 -x +\frac {\tan \left (\frac {\ln \left (x \right )}{2}\right )+1}{1+\tan \left (\frac {\ln \left (x \right )}{2}\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 36

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

\[ y(x)\to \frac {1}{2} (\sin (\log (x))+\cos (\log (x))+2 ((-1+c_3) x+(x-c_1) \log (x)+c_2)) \]