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Compute the Wronskian for the set of three functions {{eq}2,e^{3Ax},4e^{4Bx} {/eq}} where A and B are constants. Determine the conditions on the constants A and B that will make the set linearly.

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Consider the function {eq}f(x) = 5 cos^2 x – 10 sin x, quad 0 leq x leq 2pi {/eq} (a) Find the interval on which the function is increasing. (b) Find the local minimum and maximum values of the.

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(a): {eq}text{det} begin{bmatrix} d & e & f\ -3a & -3b & -3c \ g – 4d & h- 4e & i – 4f end{bmatrix}. {/eq} (b): {eq}text{det} begin{bmatrix} a + b & d + e & g + h\ 2c & 2f & 2i \ b & e & h &.

Suppose that {eq}y_c=C_1y_1+C_2y_2 {/eq} is a solution to the homogeneous equation {eq}y”+b(x)y’+c(x)y=0 {/eq}. Then a particular solution of {eq}y”+b(x)y’+c(x)y=f(x) {/eq} will have the form.