 Hi and welcome to the session. Today I am going to help you with the following question. Question says the general solution of the differential equation dy upon dx is equal to e raised to the power x plus y is we have to choose the correct answer from A, B, C and D. Let us now start with the solution. Now given differential equation is dy upon dx is equal to e raised to the power x plus y. Now this implies dy upon dx is equal to e raised to the power x multiplied by e raised to the power y. We know e raised to the power x plus y can be written as e raised to the power x multiplied by e raised to the power y. Here we have applied this rule of exponents. Now separating the variables of this equation we get dy upon e raised to the power y is equal to e raised to the power x dx. Now integrating both the sides we get integral of dy upon e raised to the power y is equal to integral of e raised to the power x dx. Now we know 1 upon e raised to the power y is equal to e raised to the power minus y. So here we can write e raised to the power minus y for 1 upon e raised to the power y and we get integral of e raised to the power minus y dy is equal to integral of e raised to the power x dx. Now first of all let us evaluate this integral. Now we will find this integral by using substitution method. So we can write put minus y is equal to t. Differentiating both the sides with respect to y we get minus dy is equal to dt. Multiplying both the sides of this equation by minus 1 we get dy is equal to minus dt. Now substituting t for minus y we get integral of e raised to the power t and we will substitute minus dt for dy. So here we will write minus dt. Now this is further equal to minus integral of e raised to the power t dt. This is further equal to minus e raised to the power t plus c we know integral of e raised to the power x dx is equal to e raised to the power x only. So integral of e raised to the power t with respect to t is equal to e raised to the power t. So here we can write e raised to the power t. Now substituting minus y for t we get minus e raised to the power minus y plus c is equal to integral of e raised to the power minus y dy. Now clearly we can see this integral is equal to minus e raised to the power minus y plus c. We will write this is equal to sign as it is. Here we will write e raised to the power x we know integral of e raised to the power x dx is equal to e raised to the power x only. Now this implies c is equal to e raised to the power x plus e raised to the power minus y. Adding e raised to the power minus y on both the sides of this equation we get this equation or we can write it as e raised to the power x plus e raised to the power minus y is equal to c. So the correct answer is A. This is the required general solution of the given differential equation and our required answer is A. This completes the session. Hope you understood the solution. Take care and have a nice day.