1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], what special case is this? A. Cauchy-Euler Equation B. Legendre Equation C. Variation of Parameters D. None of the choices...

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Extracted text: 1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], what special case is this? A. Cauchy-Euler Equation B. Legendre Equation C. Variation of Parameters D. None of the choices 2. Given:[(4x + 3)²D? – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], transform it to z. A. 64(D² – D+)y = 16e²²sec²z B. (D² – 4D + 4)y = e2# sec²z C. 64(D² – D+)y = 16e2# sec²2z D. (D? – 4D + 4)y = e2# sec²2z 3. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the transformed equation in z. A. (D3 – 6D² + 11D – 12)y = 2e4z + z B. (D³ – D² + 11D – 12)y = 2e*z + Inz C. (D³ – 6D² + 11D – 12)y = e2z + z D. (D³ – D² + 11D – 12)y = 2e** + z %3D 4. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation. A. m = 3,2 + v2i B. m = 1,4 ± V10i C. m = 4,1 ± V10i D. m = 4,1 t /2i 5. Given: x³y" – 3x²y" + 6xy' – 12y = 2x* + Inx , write the complementary solution in x. Ye = C;x³ + x²[c2cosv2x + c3sin/2x] B. Ye = c,x + x*[c2cosv10x + c3sinv10x] A. C. y. = C,x* + x[c2cosv10x + c3sin/10x] D. Ye = C1x* + x[c2cosv2x + c3sinvZx]