8.11.37 problem 60

Internal problem ID [905]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 60
Date solved : Wednesday, February 05, 2025 at 04:44:02 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: 0.008 (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)
 

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

✓ Solution by Mathematica

Time used: 0.018 (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]
 

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