83.26.16 problem 16

Internal problem ID [19340]
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 : 16
Date solved : Tuesday, January 28, 2025 at 01:34:35 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y&=x +\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

dsolve(x^4*diff(y(x),x$4)+2*x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x+ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )^{4} x}{24}+\ln \left (x \right )+4+c_{1} x +c_{2} x \ln \left (x \right )+c_3 x \ln \left (x \right )^{3}+c_4 \ln \left (x \right )^{2} x \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 44

DSolve[x^4*D[y[x],{x,4}]+2*x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==x+Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} x \log ^4(x)+\log (x)+c_1 x+c_4 x \log ^3(x)+c_3 x \log ^2(x)+c_2 x \log (x)+4 \]