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y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64
Solution: As we noticed in previous illustration the function is a solution and we can after that notice that:
And therefore this solution also meets the initial conditions of y (4) = 1/8 , and y'(4) = -3/64.
Actually, y (x) = x-3/2 is the merely solution to this differential equation which satisfies such two initial conditions.
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Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/16 - 3/4 = -11/16 implies x = (-1+i(11)^(1/2))/4 and its conjugate.
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
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