83.37.4 problem 4

Internal problem ID [19449]
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 (B) at page 128
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:43:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]-2*b*x*D[y[x],x]+b^2*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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