83.30.7 problem 7

Internal problem ID [19386]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:36:30 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve((1+x^2)*diff(y(x),x$2)+x*diff(y(x),x)+a*x=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} \operatorname {arcsinh}\left (x \right )-a x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 17

DSolve[(1+x^2)*D[y[x],{x,2}]+x*D[y[x],x]+a*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -a x+c_1 \text {arcsinh}(x)+c_2 \]