DSolve.md

May 1, 2026 · View on GitHub

DSolve

DSolve(equation, f(var), var)

attempts to solve a linear differential equation for the function f(var) and variable var.

See:

Examples

>> DSolve({y'(x)==y(x)+2},y(x), x)
{{y(x)->-2+E^x*C(1)}}

>> DSolve({y'(x)==y(x)+2,y(0)==1},y(x), x)
{{y(x)->-2+3*E^x}}

>> DSolve(y''(x) == 0, y(x), x)
{{y(x)->C(1)+x*C(2)}}     

>> DSolve(y''(x) == y(x), y(x), x)
{{y(x)->C(1)/E^x+E^x*C(2)}}

>> DSolve(y''(x) == y(x), y, x)
{{y->Function({x},C(1)/E^x+E^x*C(2))}}

DSolve can also solve basic PDE

>> DSolve(D(f(x, y), x)/f(x, y) + 3*D(f(x, y), y) / f(x, y) == 2, f, {x, y}) 
{{f->Function({x,y},E^(2*x)*C(1)[-3*x+y])}}

>> DSolve(D(f(x, y), x)*x + D(f(x, y), y)*y == 2, f(x, y), {x, y}) 
{{f(x,y)->2*Log(x)+C(1)[y/x]}}
        
>> DSolve(D(y(x, t), t) + 2*D(y(x, t), x) == 0, y(x, t), {x, t}) 
{{y(x,t)->C(1)[1/2*(2*t-x)]}}

DSolveValue, Factor, FindRoot, NRoots,Solve

Implementation status

  • ☑ - partially implemented

Github