Differential Equations and Linear Algebra, 4th Edition

Section 7.3

1. 1. $x_1(t)=c_1{e}^{-t}+c_2{e}^{3t}\text{,}{x}_2(t)=-c_1{e}^{-t}+c_2{e}^{3t}$

   

2. 2. $x_1(t)=c_1{e}^{-t}+3c_2{e}^{4t}\text{,}{x}_2(t)=-c_1{e}^{-t}+2c_2{e}^{4t}$

3. 3. General solution $x_1(t)=c_1{e}^{-t}+4c_2{e}^{6t}\text{,}{x}_2(t)=-c_1{e}^{-t}+3c_2{e}^{6t}$ Particular solution $x_1(t)=\frac{1}{7}(-e^{-t}+8e^{6t})\text{,}{x}_2(t)=\frac{1}{7}(e^{-t}+6e^{6t})$.

4. 4. $x_1(t)=c_1{e}^{-2t}+c_2{e}^{5t}\text{,}{x}_2(t)=-6c_1{e}^{-2t}+c_2{e}^{5t}$

   

5. 5. $x_1(t)=c_1{e}^{-t}+7c_2{e}^{5t}\text{,}{x}_2(t)=c_1{e}^{-t}+c_2{e}^{5t}$

   

6. 6. General solution $x_1(t)=5c_1{e}^{3t}+c_2{e}^{4t}$, $x_2(t)=-6c_1{e}^{3t}-c_2{e}^{4t}$ Particular solution $x_1(t)=-5e^{3t}+6e^{4t}$, $x_2(t)=6e^{3t}-6e^{4t}$.

7. 7. $x_1(t)=c_1{e}^t+2c_2{e}^{-9t}\text{,}{x}_2(t$