83.26.4 problem 4

Internal problem ID [19328]
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 : 4
Date solved : Tuesday, January 28, 2025 at 01:34:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x^4,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 \left (x^2+2 c_2 x+2 c_1\right ) \]