Solving Linear Differential Equations
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Use the formulas for 'solving a linear differential equation'.
1) Write the equation in standard form y' = P(x)y = Q(x)
2) Find the integrating factor u(x) = e^( ? P(x) dx)
3) Evaluate the integral to find the general solution
y = (1/u(x) ? Q(x) u(x) dx
4) Satisfy whatever initial condition is included.
1) y' + (2x - 1)y = 0, initial condition is y = 2 when x = 1
2) xy' - 2y = -(x^2), initial cond. is y = 5 when x = 1
3) (x^2)y' - 4xy = 10, initial condition is y = 10 when x = 1.
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Solution Summary
The solution solves linear differential equations.
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