Mathematics - Differential Equation Question with Solution | TestHub

$\because f^{\prime \prime }(x)-g^{\prime \prime }(x)=0$ Integrating, $f^{\prime }(x)-g^{\prime }(x)=c\Rightarrow f^{\prime }(1)-g^{\prime }(1)=c\Rightarrow 4-2=c\Rightarrow c=2$ $\therefore f^{\prime }(x)-g^{\prime }(x)=2;$ Integrating, $f(x)-g(x)=2x+c_1$ $\Rightarrow f(2)-g(2)=4+c_1\Rightarrow 9-3=4+c_1\Rightarrow c_1=2\therefore f(x)-g(x)=2x+2$ At $x=3/2,f(x)-g(x)=3+2=5$