60.3.271 problem 1276

Internal problem ID [11281]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1276
Date solved : Monday, January 27, 2025 at 11:05:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 30

dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-(4*x^2+1)*y(x)-4*(x^3)^(1/2)*exp(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sqrt {x^{3}}\, {\mathrm e}^{x}}{2 x}+\frac {\sinh \left (x \right ) c_{2} +\cosh \left (x \right ) c_{1}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 55

DSolve[-4*E^x*Sqrt[x^3] - (1 + 4*x^2)*y[x] + 4*x*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x \sqrt {x^3} (2 x-1)}{4 x^2}+\frac {c_1 e^{-x}}{\sqrt {x}}+\frac {c_2 e^x}{2 \sqrt {x}} \]