7.11.58 problem 60

Internal problem ID [379]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 60
Date solved : Wednesday, February 05, 2025 at 03:26:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y&=8 x^{{4}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 20

dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+3*y(x)=8*x^(4/3),y(x), singsol=all)
 

\[ y = x^{{3}/{2}} c_2 +c_1 \sqrt {x}-\frac {72 x^{{4}/{3}}}{5} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 31

DSolve[4*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+3*y[x]==8*x^(4/3),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} \sqrt {x} \left (-72 x^{5/6}+5 c_2 x+5 c_1\right ) \]