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Differential Equations Solver

LivePhysics

Solution Curve

xy

Parameters

Results

Root Classification
Complex conjugate roots
Roots
r1 = 0 + 1i, r2 = 0 - 1i
General Solution
y = e^{0x}(C_1 \cos 1x + C_2 \sin 1x)
Particular Solution
y = e^{0x}(1 \cos 1x + 0 \sin 1x)

Step-by-Step Solution

1. Write the characteristic equation

1r2+0r+1=01r^2 +0r +1 = 0

2. Compute discriminant

Δ=b2−4ac=(0)2−4(1)(1)=−4\Delta = b^2 - 4ac = (0)^2 - 4(1)(1) = -4

3. Find complex roots

r=0±1ir = 0 \pm 1i

4. General solution

y=e0x(C1cos⁡1x+C2sin⁡1x)y = e^{0x}(C_1 \cos 1x + C_2 \sin 1x)

5. Particular solution (IVP)

y=e0x(1cos⁡1x+0sin⁡1x)y = e^{0x}(1 \cos 1x + 0 \sin 1x)

Reference Guide

Free ODE solver for separable, first-order linear, and second-order constant coefficient differential equations with slope fields and step-by-step solutions.

Separable ODEs

primary

First-Order Linear

secondary

Characteristic Equation

tertiary

Slope Fields