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Enter an equation, copy/paste, or upload an image to solve differential equations.
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This differential equation solver helps to solve differential equations involving functions and their derivatives. Our tool supports first-order, second-order, and higher-order differential equations, providing step-by-step solutions. You can input problems manually, choose from a library of common equations, or upload an image of the equation for processing.
“Differential Equation is a mathematical equation that relates one or more functions to its derivatives.”
General Form:
\( F\left(x, y, \frac{dy}{dx}, \frac{d^2y}{dx^2}, \dots, \frac{d^n y}{dx^n}\right) = 0 \)
Explanation:
A differential equation describes the relationship between a quantity and its rate of change. Within this equation, function represents physical quantities while their derivatives show how those quantities change over time.
Solve the differential equation: dy / dx = 3y
Identify Type: This is a first-order linear differential equation.
Separate Variables: 1 / y dy = 3 dx
Integrate both sides: ∫1 / y dy = ∫ 3 dx
ln |y| =3x + C
Solve for y: y = e³ˣ ⁺ ᶜ = Ce³ˣ , Where C = eᶜ (simplified constant).
Apply Initial Condition: if y (0) = 2
2 = Ce⁰ ⟹ C = 2
Final Solution = y = 2e³ˣ
Our online Differential Equations Calculator provides you with a general solution of differential equations, allowing you to use it again and solve as many questions as you want.
It contains one or more derivatives of a function with respect to a single independent variable.
dy / dx + y = ex
Where y is the dependent variable, x is the independent variable.
A partial differential equation (PDE) involves partial derivatives of a function with respect to multiple independent variables.
∂u / ∂t = D ∂²ᵘ/ ∂x²
The equation where the dependent variable and its derivatives appear only to the first power and are not multiplied together.
aₙ(x) * (dⁿ y) / (dxⁿ) + aₙ₋₁(x) * (d⁽ⁿ⁻¹⁾ y) / (dx⁽ⁿ⁻¹⁾) + ... + a1(x) * (dy/dx) + a₀(x) * y = f(x)
Where:
an(x) , an-1(x) and a0(x) are functions of x and f(x) is given function.
The equation where the dependent variable or its derivatives appear with powers greater than one or are multiplied together.
(dy/dx)² + y² = x
The equation where all terms involve the dependent variable or its derivatives.
d²y/dx² + 5 dy/dx + 6y = 0
A non-homogeneous differential equation has a nonzero function on the right-hand side.
d²y/dx² + 5 dy/dx + 6y = (e)ˣ
(The right-hand side is eˣ, making it non-homogeneous.)
Yes, this differential equation calculator provides you with stepwise solutions for solving equations.
Our Differential Equation Calculator allows you to upload images for automatic recognition and solving.
Some common methods to solve differential equations include separation of variables, integration factors, characteristic equations, Laplace transform, and numeric methods.
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