Question

Encontre uma função y(x) que resolve o problema de valor inicial a seguir:​

Answer 1

$\sf\dfrac{dy}{dx}=e^x+1~~y(1)=e\\\sf dy=(e^x+1)dx\\\displaystyle\sf\int dy=\int(e^x+1)~dx\\\sf y(x)=e^x+x+k\\\sf y(1)=e^{1}+1+k\\\sf\diagup\!\!\!e+1+k=\diagup\!\!\!e\\\sf k+1=0\\\sf k=-1\\\large\boxed{\boxed{\boxed{\boxed{\sf y(x)=e^x+x-1}}}}\blue{\checkmark}$