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**Unformatted text preview: **exists. y = 1-2 x y , y > with y (1) =-2 (2.2.16) Solve the given initial value problem and ﬁnd the largest interval on which the solution exists. y = x ( x 2 + 1) 4 y 3 with y (0) =-1 √ 2 (2.1.20) Solve ty + (1 + t ) y-t = 0 , y (ln 2) = 1 , t > (2.2.34) Solve y =-(4 x + 3 y ) (2 x + y ) 1 (2.1.1) Solve y + 3 y = t + e-2 t (7.2.13), (7.2.14) Find the inverse of (a) A = 1 1-1 2-1 1 1 1 2 (b) A = 1 2 1-2 1 8 1-2-7 (7.3.16) Find all eigenvalues and eigenvectors of A = ± 3-2 4-1 ² (7.3.4) Completely solve the given system of equations x 1 + 2 x 2-x 3 = 0 2 x 1 + x 2 + x 3 = 0 x 1-x 2 + 2 x 3 = 0 (2.3.3) Refer text. (2.3.24) Refer text. (2.4.2) Find intervals of existence of solution of t ( t-4) y + y = 0 , y (2) = 1 2...

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