Application to ordinary linear differential equations and engineering problems

The value of differential operator d2y/dx2 of the equation x2+e3x-y2=0
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The complementary function of the differential equation 3y’’-12y=0
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The complete integral of the differential equation 2y’’-3y=-cosx
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Let T(y)=r be a linear map equation, where T:F→F is the operator defined as T=D2+PD+QI and P, Q∈R. Then its solution is
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The function c1e5x+c2e4x+ex is the complete integral and then it satisfies which of the following differential equation
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