83.26.3 problem 3

Internal problem ID [19327]
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 : 3
Date solved : Tuesday, January 28, 2025 at 01:34:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=x^4,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+\frac {\ln \left (x \right ) c_{1}}{x^{2}}+\frac {x^{4}}{36} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^6+72 c_2 \log (x)+36 c_1}{36 x^2} \]