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Difficult first order linear differential equation

Dhamnekar Winod

Active member
Nov 17, 2018
149
Hello, I want to solve the following differential equation. $y'=\dfrac{x^3-y^3}{x-y}$. How to solve it?
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,198
Wolfram Development Platform (essentially Mathematica) gives a horrendous answer: extremely complicated with Hermite $H_n(x)$ functions and the hypergeometric $_1F_1$ function. In what context did this problem come up, and what have you tried?
 

Dhamnekar Winod

Active member
Nov 17, 2018
149
Wolfram Development Platform (essentially Mathematica) gives a horrendous answer: extremely complicated with Hermite $H_n(x)$ functions and the hypergeometric $_1F_1$ function. In what context did this problem come up, and what have you tried?
I got the following answer from my differential equation solver.

\[y(x)=\frac{x^3}{6}(C_1(C_1+1)+3C_1+2)+\frac{x^5}{120}(C^3_1+C_1(74C_1+9)+31C_1+8)+C_1+C_1x+\frac{3C_1x^2}{2}+\frac{C_1x^4}{12}(C_1+4)+\mathcal{O}\]
 
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karush

Well-known member
Jan 31, 2012
2,886
You can reduce the expression to this

y'=x^2 + x y + y^2