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Solutions of Differential Equations Calculator

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Example
Created on 2024-06-20Asked by Daniel Ramirez (Solvelet student)
Find the general solution of the differential equation y′′−y=0y'' - y = 0.

Solution

To find the general solution of the differential equation y′′−y=0y'' - y = 0: 1. **Find the characteristic equation:** r2−1=0. r^2 - 1 = 0. 2. **Solve the characteristic equation:** r2=1  ⟹  r=±1. r^2 = 1 \implies r = \pm 1. 3. **General solution:** y(x)=c1ex+c2e−x, y(x) = c_1 e^x + c_2 e^{-x}, where c1c_1 and c2c_2 are arbitrary constants. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Jack Roberts on Solvelet
1. Find the general solution of the differential equation y′′−y=0 y'' - y = 0 .2. Apply separation of variables to solve the differential equation y′=2x+3y y' = 2x + 3y , y(0)=1 y(0) = 1 .,
DefinitionThe solutions of them are functions which satisfy the corresponding relations. There are general solutions consist of arbitrary constants and the particular solutions which specify the values of the these constants. Ex ans: dy/dx=ky general solution is y=Cekx where C is arbitrary constant
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