83.41.5 problem 2 (iv)

Internal problem ID [19485]
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 at end of chapter VIII. Page 141
Problem number : 2 (iv)
Date solved : Tuesday, January 28, 2025 at 01:46:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 33

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

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