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(3x+y-4)dx+(x+y-2)dy=0
solve power series solution
y'' - (x+1) y' -y = 0
solve power series solution
y'' - 2xy' + y = 0
Solve;Β Β (π§ 2 β 2π¦π§ β π¦ 2 )π + (π₯π¦ + π§π₯)π = π₯π¦ β π§x
Solve : π₯(π¦ 2 β π§ 2 )π + π¦(π§ 2 β π₯ 2 )π = π§(π₯ 2 β π¦ 2 )Β
Form the PDE by eliminating the arbitrary function from π ( π₯βπ¦ π¦βπ§ , π₯π¦ + π¦π§ + π§π₯) = 0.
Form the PDE by eliminating the arbitrary constants from β1 + π 2 log(π§ + βπ§ 2 β 1) = π₯ + ππ¦ + b .
In a two-dimensional electric eld, it is known that the electric eld 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.
Use Laplace transform to solve the differential equationy
β²β²β2yβ²β3y=0yβ³β2yβ²β3y=0
with the initial conditionsΒ y(0)=2y(0)=2Β andΒ yβ²(0)=β1yβ²(0)=β1Β andΒ yΒ is a function of timeΒ t.
(D2-D')z=ex-ysin(x+2y)
