83.26.19 problem 19

Internal problem ID [19343]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 01:34:59 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 45

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

\[ y \left (x \right ) = \frac {2 \ln \left (x \right )^{3} x^{2}-3 \ln \left (x \right )^{2} x^{2}+24 c_{2} x^{2} \ln \left (x \right )+24 c_3 \,x^{2}+6 c_{1}}{24 x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 45

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

\[ y(x)\to \frac {1}{48} x \left (4 \log ^3(x)-6 \log ^2(x)+6 \log (x)-3\right )+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \]