# How to solve differential equations on Matlab and Octave

To solve a differential equation on Matlab and Octave use the instruction dsolve()

dsolve(eq, cond)

The first parameter (eq) is the differential equation.

The second parameter (cond) is the initial condition.

Note. In Octave the dsolve() function requires the installation and loading of the Symbolic module.

## Examples

Example 1

Define a y (x) function as a symbol using the command syms

syms y(x)

Define the differential equation y '' - y = 0 of the second order in a variable

Write the derivatives of the function y (x) using the command diff(f,n)

eq = diff(y,x,2) - diff(y,x,1) == 0

Solve the differential equation using the command dsolve(eq)

S = dsolve(eq)

The general solution of the differential equation is

y(x)=c1 + c2e^x

The result is assigned to the variable S.

Example 2

Define the function symbol via the command syms

syms y(x)

Define the differential equation

eq = diff(y,x,2) - diff(y,x,1) == 0

Define the initial condition

cond = y(0) == 3

Solve the differential equation with respect to the initial condition using the command dsolve(eq,cond)

S = dsolve(eq,cond)

The solution of the differential equation is

y(x)=3e^x

The result is assigned to the variable S.

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Calculus in Matlab/Octave