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how to solve y''-y'-12y=e4x
dx/y+1 =dy/X+1=dz/z
y"-4y'+13y=sin2t
Solve (D2+2DD'+D'2)z=cos(x+2y)+ex-2y.
In a two-dimensional electric field, it is known that the electric field lines and equipotential lines are orthogonal to each other. Given that the electric lines of force of two opposite charges of the same strength are circles passing through the points (0, 3) and (0, -3). Determine the following:
a. Obtain the equipotential lines
b. Trace the given electric lines and the orthogonal equipotential lines.
Reduce the second order linear differential equation d²y/dt²-7dy/dt+10y=0 to linear system of first order differential equation and hence solve the system of ODE's
X²(d²y/dx²)-4x(dy/dx)+6y=42/x⁴
Solve (X^2-y^2-Z^2)p+2xyq=2xz
z(x+y)p+z(x-y)q=x^2+y^2
Find the general solution of the following differential equation x dy / dt - 4y = x^5 e^x
