83.40.7 problem 7

Internal problem ID [19479]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (E) at page 140
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:46:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y&=-4 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x$2)-2*x*(1+x)*diff(y(x),x)+2*(1+x)*y(x)=-4*x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (c_{1} {\mathrm e}^{2 x}+c_{2} +2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]-2*x*(1+x)*D[y[x],x]+2*(1+x)*y[x]==-4*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x \left (4 x+c_2 e^{2 x}+2+2 c_1\right ) \]