# How do I solve?

**URL:** <https://community.wolfram.com/t/how-do-i-solve/2208>\
**Category:** Questions\
**Tags:** wolfram-alpha, calculus\
**Created:** [May 14, 2014, 10:05pm UTC](https://community.wolfram.com/t/how-do-i-solve/2208 "2014-05-14T22:05:22Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![nabel](https://avatars.discourse-cdn.com/v4/letter/n/7ab992/32.png) [@nabel](https://community.wolfram.com/u/nabel)\
**Post date:** [May 14, 2014, 10:05pm UTC](https://community.wolfram.com/t/how-do-i-solve/2208/1 "2014-05-14T22:05:22Z")

</div>

I am suppose to solve (fg)‘=f’g’ given f(x)=e^(x^2). I am suppose to find g(x)

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<div class="post-metadata">

**Author:** ![fkampas](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/fkampas/32/41217_2.png) [@fkampas](https://community.wolfram.com/u/fkampas)\
**Post date:** [May 14, 2014, 10:49pm UTC](https://community.wolfram.com/t/how-do-i-solve/2208/2 "2014-05-14T22:49:55Z")

</div>

```auto
In[1]:= DSolve[D[Exp[x^2]*g[x], x] == Exp[x^2] g'[x], g[x], x]

Out[1]= {{g[x] -> 0}}

```

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<div class="post-metadata">

**Author:** ![melvyn11](https://avatars.discourse-cdn.com/v4/letter/m/94ad74/32.png) [@melvyn11](https://community.wolfram.com/u/melvyn11)\
**Post date:** [May 15, 2014, 3:18pm UTC](https://community.wolfram.com/t/how-do-i-solve/2208/3 "2014-05-15T15:18:03Z")

</div>

```auto
f[x_] := Exp[x^2]

DSolve[D[f[x] g[x], x] == f'[x] g'[x], g[x], x] // Simplify

{{g[x] -> E^(-(1/2) + x) Sqrt[-1 + 2 x] C[1]}}

```

Since E^(-(1/2)+x) can be rewritten as e^-(1/2) e^x , the e^-(1/2) can be included within the arbitrary constant and the solution is

g = C\_1 e^x Sqrt[2x-1]

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<div class="post-metadata">

**Author:** ![sblinder](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sblinder/32/17861_2.png) [@sblinder](https://community.wolfram.com/u/sblinder)\
**Post date:** [May 15, 2014, 4:17pm UTC](https://community.wolfram.com/t/how-do-i-solve/2208/4 "2014-05-15T16:17:55Z")

</div>

```auto
In[3]:= f[x_] := Exp[x^2]

In[4]:= DSolve[f[x] g'[x] + f'[x] g[x] == f'[x] g'[x], g[x], x]

Out[4]= {{g[x] -> E^(1/2 (-1 + 2 x + Log[-1 + 2 x])) C[1]}}

In[5]:= Simplify[%]

Out[5]= {{g[x] -> E^(-(1/2) + x) Sqrt[-1 + 2 x] C[1]}}

```